Thursday's primaries saw Livni win by an extremely narrow vote of 1.1% – a total of 431 votes.
"The results of the primaries are problematic, they show too many irregularities," said Elkin. "I'm willing to take this to court if necessary."
Elkin, who supported Transportation Minister Shaul Mofaz's bid for the Kadima premiership, and other members of Mofaz's campaign headquarters petitioned Kadima's elections committee on the very night of the primaries, demanding a recount, but were denied.
Mofaz's attorney, Yehuda Weinstein, was quoted Thursday as saying that given how close the race and its results were, he would recommend his client appeal the results.
Livni, said Weinstein, may have won by 431 votes, but a Rahat ballot, which was disqualified by the elections committee after exhibiting irregularities, was one of 430 votes. "You can't govern Israel by a one-vote win. It's not right," he stated.
Mofaz himself, however, seemed to have resigned with the results, enough to call the newly-elected chairwoman on Friday and offer his congratulations.
Elkin himself chose to protest the results by not attending Kadima's faction meeting on Friday, telling Ynet that "this is no time for victory celebrations. The wounds are still raw and many activists feel cheated by the results."